Thursday, 28 July 2016

Take The Gauss Challenge!

All of the really clever stuff behind digital audio is just mathematics, pure and simple.  I’ve said before - and will say again - that mathematics is the purest of the pure sciences, and for that reason is often separated out from the rest of science.  The principal differentiator is that in the pure sciences the ultimate standard of correctness is measured in terms of empirical evidence, whereas in mathematics it lies in absolute proof.  Also - somewhat more esoteric in concept - scientific postulates usually start with a simple everyday observation, and proceed from there to both break it down into its component constructs and expand it into more elaborate implications.  By comparison, mathematics begins at ground zero.  It starts by defining the quantities ZERO and ONE, plus the concept of ADDITION, and builds upwards from there.

Mathematics, like Physics, also has the capacity to lead us down some mind-bending rabbit-holes.  One such example is Kurt Gödel’s famous Incompleteness Theorem.  Among other things, this theorem [a theorem is an axiom which has been proven mathematically to be correct - as opposed to a theory, which is an unproven postulate] states that there are some things that are mathematically correct, but which are fundamentally incapable of being proven.  Furthermore, he shows that it is impossible to prove that any given unprovable theorem is indeed unprovable.  But we don’t need to go there ….

I should observe that while I talk about mathematics in such glowing terms, I myself am a physicist.  I was equally qualified to study physics or mathematics at university (music too, for that matter), and wisely chose physics.  While at university I could keep up with my two mathematician friends for most of my first year, but by the second year it became obvious that what they were studying went way over my head.  Waaaaay over.  Good call.

One of the greatest mathematicians ever was a German named Carl Friedrich Gauss.  A famous true story is told of him, one against which you might be interested to try to measure yourself.  There is a nice, simple formula that gives you the sum of all integer numbers (1 + 2 + 3 + 4 + 5 +, … etc) up to any arbitrary number N.  That formula is N*(N+1)/2.  My challenge to you is to prove it.

The proof is erroneously attributed to Gauss.  As a 10-year old boy attending school in 1787, Gauss’s class was asked by their teacher to add up all the whole numbers between 1 and 100.  This gave the teacher some spare time to take a nap.  However, after ten minutes Gauss woke him up with the correct answer - 5,050.  He couldn’t be bothered to do all the adding up, and so had derived the above formula on the spot.  I don’t know about you, but I had not even been introduced to algebra at age 10!

In actual historical fact, the teacher - one Herr Buttner - was not looking to take a nap, but wanted to prepare his pupils’ mindset so that when he subsequently presented them with the formula they would better appreciate its worth and value.  A good teacher, I think!  Astonished by young Gauss’s precocious genius, he became his personal champion and was largely responsible for much of the young man’s early advancement.

The proof itself is in fact a deceptively simple one, which almost anyone could understand, and easily teach to others.

So I won’t bother to repeat it here :)

Wednesday, 20 July 2016

OS X 10.11.6 & iTunes

I have been using the latest combination of OS X 10.11.6 and iTunes for a day or so now, and have encountered no problems.  BitPerfect users ought to be able to apply these two updates with confidence.

Tuesday, 12 July 2016

Your Competitors are your Best Friends

I want to tell you a true story, but I’m going to change everything that identifies the actual participants.  It’s about two companies who saw each other as their biggest competitors.  There was no love lost between them, not to mention countless law suits and counter-suits.  These were large and professional public listed companies, one with hundreds and the other with thousands of employees.  Professionally managed by people with more PhDs and MBAs than you can shake a stick at.  But still …

The global market for ‘Widgets’ is $20-50 Billion dollars per year and growing, and is served by several of the world’s largest international corporations.  Widgets are manufactured in colossal volumes on highly automated production lines which run 24/7.  The manufacturing process is a multi-stage line, with each stage comprising its own dedicated machine tool.  One of these stages is the ‘Widget Tuning’ stage where the performance of each individual ‘Widget’ is precisely ’tuned’ to very tight specifications.

Widget tuning machines are evaluated against three broad parameters - (i) the precision with which they can tune a Widget, (ii) the net throughput with which they can tune Widgets, and (iii) their overall cost of ownership.  The preferred technology for Widget tuning was known as OWT (Optical Widget Tuning), and there were two manufacturers which supplied OWT machines to the global Widget industry - Opticorp, and General Optics International (GOI).  The total worldwide market for OWT machines varied between $200 and $500 Million annually, and was typically shared 60:40 between Opticorp and GOI, with both vendors generating excellent margins on these product lines.

Widget manufacturers appreciated having two vendors for these expensive manufacturing tools, which sell at up to a million dollars apiece and require comprehensive and reliable support and maintenance.  Although the market is quite a large one, it isn’t really large enough to support much more than two vendors considering that the barriers to entry are very substantial.  What would happen was, as Opticorp began to stretch their lead in market share, GOI would focus on new technology resulting in improved Widget tuning performance, and would gradually claw back market share.  Being the market leader, Opticorp would be more reluctant to risk investing in new technology, but would eventually be obliged to do so to avoid the risk of losing their dominant position.  And if neither vendor produced a compellingly differentiated product, the Widget manufacturers would start to pressure them on price.

Overall this ongoing competitive situation was good for the Widget manufacturers.  The Widget tuning process was an effective one for them, and they had two highly reliable vendors that they could play off one against the other to keep them both sharp.  But Optical Widget Tuning was not their only option.  A new technology called Electrical Widget Tuning (EWT) was waiting in the wings.  It had the potential to be at least as effective as OWT, but required other changes to be made to the overall design of the Widgets to accommodate it.  But so long as OWT remained viable there was no pressing need to abandon it.

So long as OWT remained viable …

Out of the blue, the CEO of GOI made a monumental strategic decision (the specifics of which are not germane to this discussion), and which put GOI deeply into debt.  No sooner was this announced than a global financial recession suddenly set in.  Within months it became evident that GOI was in desperate financial straits, and talk of possible bankruptcy was in the air.  And indeed, the following summer GOI went under.  Attempts to sell off their OWT business came to nought as at first they demanded too much for it, and later were forced to lay off so many of the key employees that there was no longer a critical mass that could form a viable acquisition.  There was great joy in the corridors of Opticorp as their bitter rival and only OWT competitor bit the dust and left the lucrative OWT market entirely to them.

In the boardrooms of the Widget manufacturers, though, things looked rather different.  With Opticorp now their sole supplier, they would have nothing with which to push back against price increases, and there would be limited incentive for Opticorp to invest in advancing their technology rather than pocketing cash.  Instead, they decided that they had no choice but to go all out to bring Electronic Widget Tuning to maturity as their preferred Widget tuning technology.

Opticorp insisted that they didn’t see this coming.  In internal meetings their product managers gave presentation after presentation showing how OWT met all Widget manufacturing requirements, how EWT would offer no advantage, and how a switch to EWT would be disruptive across the board.  In short, gentlemen, EWT was a load of hot air and would never happen.  But happen it did, despite Opticorp’s technical analysis being pretty well on the money.  What it utterly failed to take into account were the strategic perspectives.  Within two years Opticorp’s OWT sales had dropped by 75%, and within another 12 months they had evaporated completely.  Shortly thereafter, Opticorp’s CEO was shown the door.

The point of this post is not to show how Opticorp could or should have responded differently.  That is actually far from simple, and would form a much more elaborate case study.  Instead it is a reflection of how events which would lead to the demise of a highly profitable $250M business within three years were greeted by whoops of celebration, and not a hint of trepidation over how it might end up playing out.  And how a proper assessment of the situation failed to be undertaken through hubris and conceit.

As I said, this is a true story, I hope accurately portrayed, and it teaches a valuable business lesson.  It really doesn’t matter what size your business is - you need competition, and you have to understand why.  Competitors keep you honest.  Without competition for your business there is no incentive for you to reduce costs, increase efficiencies, and improve service.  There is no incentive for you to invest in making your product better.  And ultimately, there is no incentive for your customers to remain interested in it.

For better or for worse, consumers at all levels - whether consumers of shampoo or OWT manufacturing tools - want to have choices.  Sometimes it is because people just feel more comfortable when they have choices - but sometimes it is because a well-considered strategy demands alternatives.  Where there is no choice there is stagnation, such as is typically the case with things like public transport.  Having competition is what keeps any business fresh.  Your competitors may want to put you out of business, and you them, but in reality they are your Best Friend.  Embrace it!

Wednesday, 6 July 2016

“Tell Them We’ve Already Got One!”

Let me describe something I was very fortunate to be able to try one time, but which very few of us will get the opportunity to experience.  I am talking of entering an anechoic chamber.

An anechoic chamber is a room specially designed for the purpose of conducting carefully calibrated acoustic measurements.  In normal rooms, any sound generated anywhere within the room will travel rapidly to all other parts of the room by bouncing off the walls (including the ceilings and floors).  Therefore, if we attempt to measure the sound in a room we very quickly find that it is impossible to distinguish between sounds which originate directly from the source and those which have travelled via multiple bounces off the room boundaries.  This is important, because these multiple signal paths cause the signal to be reinforced, cancelled out, or anything in between, thereby rendering many forms of measurement entirely useless.

The solution is to create a room in which sound waves, when they hit one of the walls (or floors, or ceilings), is instantly and totally absorbed and none of it is reflected back into the room.  Such a room generates no echoes, and is therefore termed ‘anechoic’.  These are particularly useful for designing things like microphones and loudspeakers, and enable detailed and accurate measurements to be performed in a way that would be virtually impossible otherwise.  You’d think that every loudspeaker manufacturer would have one, but they don’t.  They all wish they did, but most of them can’t afford such a preposterously expensive luxury.  The best they can hope to do is rent time in somebody else’s (most likely in a university research centre, or some other such institution).

What is particularly instructive is to get somebody to step into an anechoic chamber for the first time, and ask them to sing a song or play an acoustic instrument.  You can bet your mortgage that they will stop singing or playing within less than a second.  What they hear are sounds so alien to them that they can’t help but stop abruptly.  It only works first time, because once you know what is going to happen you aren’t so taken aback.

The sound of a voice or an instrument in an anechoic chamber is so utterly unlike anything you have ever heard before that it just stops you dead in your tracks.  Same goes for a loudspeaker playing in an anechoic chamber.  It is a totally dry sound, devoid of all character, expression, depth, or life.  After stopping abruptly, the second thing you will do is lick your lips, because the sound is so dry, so arid, so utterly parched, that it seems to draw the moisture from every pore in your body.  It is a profoundly unnatural environment.

And yet, the sound of a voice or an instrument in an anechoic chamber is the most accurate representation of that sound.  That is precisely what that voice or instrument actually sounds like.  Only the sounds travelling directly from the source to the listener will reach the listener.  All other sounds will be totally absorbed as soon as they hit any of the walls.  This is as accurate as it gets.

Outside of the anechoic chamber, the sound you hear is the sound of that instrument playing in a given room.  The difference between what you heard inside the chamber and outside is the contribution of the room to the sound.  That contribution is colossal.  Indeed it is fundamental to how we perceive the sound.  The magnitude of the difference serves to ram home the point that everything we hear every day is the product of the various sound sources modified by the environments in which we both exist.  The same orchestra, for example, playing in two different concert halls often sounds like two different orchestras.

This is important to grasp, because it serves to illustrate the futility of one of the holy grails of the audio industry - or more precisely of many of the critics who presume to influence the industry as to what it should be doing.  This particular sacrament requires that the goal of a high-end audio system is to recreate the sound of the original instrument.  But the sound of the original instrument is the desiccated sound from the anechoic chamber, and that is not what people want to hear.  What they want to hear is the sound of the original instrument played in the original location, but they want to replay it in a different location.

That presents us with two separate philosophical problems.  First, how are we to know what the original performance actually did sound like in the original location?  Unless we were there at the time, we can’t.  Second, our loudspeakers are located in their own separate and different acoustic environment.  If ‘simply’ reproducing the musical instruments themselves in our own listening environment is challenging enough, it is a different challenge entirely to reproduce the audio environment of one room inside an entirely different room.  Just consider recording a violin in an anechoic chamber, and then trying to reproduce the sound of that anechoic chamber in your own listening room.  Take it from me, it is not possible to come even close.

So what is it we actually want from our systems?  I believe we just want to be convinced.  We listen to something and ask ourselves how convinced we are by the illusion that our system has created.  The best sound systems do recreate a good illusion of a complete acoustic space.  However, for most - if not all - of our recordings, we have no idea whether that space is the same as the one in which the recording was made.  But if we can be convinced by what we hear - transported into a listening experience - surely that is all we can realistically ask.  I have long ago stopped asking myself if the sound I was getting was ‘correct’.  There is no ‘correct’.  Nowadays I ask only whether - and to what degree - I am convinced.

I think this goes some way to explaining the pangs that most of us face as we periodically upgrade our sound systems.  Critics charge that we are never satisfied, so why bother in the first place.  And there is a lot of truth to that.  We buy a system, express our happiness with it, listen to it for a few years, and then upgrade it.  Rinse and repeat.  With each new system, not only are we satisfied that it is better than the old system, but suddenly the old system - to which we were formerly devoted - is now somehow inadequate and no longer lovable (other than through the distorted lens of nostalgia).  We cannot go backwards down the audio path and still retain the same sense of joy that powered us on the way up.  All this, of course, assumes that the upgrade path was always followed wisely and judiciously.

What is happening, I suggest, is that on each path up the upgrade chain we are re-setting the bar against which our system’s ability to ‘convince’ us is measured.  The whole point of a significant upgrade is to significantly enhance your system’s ability to convince you that it is better recreating the original soundscape.  If it can pull that off, it will permanently re-set your bar.  It now takes an even greater level of fidelity to improve upon the trick of convincing us.  Once you’ve heard something, you can’t ‘unhear’ it.

When I was a young man just setting out with this hobby, most critical evaluation of audio systems - particularly loudspeakers - was focussed on the degree to which the sound took on identifiable tonal colourations.  And indeed, back in those days colourations were indeed a dominant factor.  One product which I recall having a particular impact in the marketplace was the Kef R104aB loudspeaker, which was noted for having particularly low levels of colouration.  I used a pair once for a few weeks and confirmed that yes, indeed, they did have a particularly uncoloured sound.  But at the end of my time with them I realized that while they were undeniably uncoloured, they didn’t seem to float my boat any more as a consequence.

I wasn’t smart enough yet for the penny to drop, but yes, shortly thereafter it did so.  I have long since realized that for my own particular musical enjoyment, tonal colourations are not a major limiting factor.  I am more than willing to put up with them if they are the price I have to pay to realize the type of performance which does float my boat, which are imaging stability and soundstaging, dynamic range (both micro and macro), and what is dismissively called PRAT (Pace, Rhythm And Timing).  With all those requirements satisfied, I am willing to put up with tonal colourations that other people might find to be cause for criticism.  Having said that, though, major advances have been made in the elimination of tonal colourations since the good old ’70’s.

So that’s where I put my stick in the ground.  As far as tonality is concerned there are no absolutes.  Tonal colour is only partially provided by the instrument itself, and is dominated by the acoustics of the room.  So when it comes to judging sound reproduction there can be no such thing as Harry Pearson’s much vaunted “Absolute Sound”.  There are no absolute points of reference other than an anechoic chamber, and nobody would want to listen to anything that sounded like that.  The most important milestone of any audiophile journey is when you finally understand what it is that YOU want out of your system - whatever that is - and achieve comfort in the knowledge that that is way more important than what some other audiophile wants out of his.

BTW, have any of you figured out the reference in this post’s title? :)